Below is a drawing of a wall that is to be covered with either wallpaper or paint. The wall is 8 ft. high and
16 ft wide. The window, mirror, and fireplace are not to be painted or papered. The window measures 18 in wide
and 14t. high. The fireplace is sit wide and 3 it. High while the mirror above the fireplace is 4 ft. wide and 2 ft.
high. Note: this drawing is not to scale)
How many square feet of wallpaper are needed to cover the wall?

84 sq. ft of the wall has to be covered with paint or wallpaper.

Step-by-step explanation:

Area of the wall = 8 × 16 = 128 ft²

Area of the window = 18/12 × 14 = 1.5 × 14 = 21 ft² (since 1 ft = 12 in)

Area of the fireplace = 5 × 3 = 15 ft²

Area of the mirror = 4 × 2 = 8 ft²

Area of the wall to be covered with paint or wallpaper = 128 - (21 + 15 + 8)

                              = 128 - 44

                              = 84 ft²

84 ft²

Step-by-step explanation:

Step 1: Find the area of the wall.

The wall is 8 ft high and  16 ft wide

A = LW

A = (16)(8)

A = 128 ft²

Step 2: Find the area of the window, fireplace, and mirror.

Window: The window measures 18 in wide  and 14 ft high

18 in = 1.5 ft

A = LW

A = (14)(1.5)

A = 21 ft²

Fireplace: The fireplace is 5 ft wide and 3 ft high

A = LW

A = (3)(5)

A = 15 ft²

Mirror: The mirror above the fireplace is 4 ft wide and 2 ft high

A = LW

A = (2)(4)

A = 8 ft²

Step 3: Add all the areas of the three objects (window, fireplace, and mirror)

A = 21 + 15 + 8

A = 36 + 8

A = 44 ft²

Step 4: Subtract the total area of the objects from the area of the wall.

A = 128 ft² - 44 ft²

A = 84 ft²

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

x/3-10=8

x/3=18

x=48